Question

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.

Answer 1

Height, h = 75 cm = 0.75 m
Density of mercury = 13600 kg/m³
g = 9.8 m/s²

In SI units, pressure = hρg = 0.75 × 13600 × 9.8 = 10 × 10⁴ N/m² (approximately)

In CGS units, pressure = 10 × 10⁴ N/m²

\[= \frac{10 \times {10}^4 \times {10}^5 \text{dyne}}{{10}^4 {\text{cm}}^2} = 10 \times {10}^5 \text{dyne}/ {\text{cm}}^2\]